The recent emergence of micro-electro-mechanical systems (MEMS) inertial sensors has made it possible to integrate a MEMS inertial measurement unit (IMU) and a global positioning system (GPS) receiver on board small missiles, rockets or the like type of projectiles or vehicles to perform strapdown navigation. Some types of missiles are imparted with a roll about a longitudinal axis in order to provide stability during flight. However, as the vehicles spins, a rapidly growing roll attitude error accumulates due to the scale factor error of the MEMS roll gyro, and the accumulated roll error eventually causes the navigation solution to become unstable. Thus, there lies a need for a method and apparatus that compensates for the accumulated roll attitude error in rolling vehicles.
Furthermore, strapdown navigation equations are linearized by small angle approximations. Therefore, the angular change in body attitude must not exceed a small amount between computation intervals, otherwise the equations become invalid. For rolling missiles, the roll angle continuously changes at a very high rate that imposes an extremely high computational rate requirement on the navigation processor. Thus, there also lies a need for a navigation system and method that allows for a reasonable computational rate requirement on the navigation processor of a rolling missile.